Coercive estimates and existence of solutions for a model of one- dimensional viscoelasticity with a non-integrable memory function
type: Item
instance of: scholarly article
title: Coercive estimates and existence of solutions for a model of one- dimensional viscoelasticity with a non-integrable memory function
zbMATH Open document ID: 0663.73024
DOI: 10.1216/JIE-1988-1-1-7
author: Michael Renardy
published in: Journal of Integral Equations and Applications
publication date: 1988-01-01T00:00:00Z
review text: In this work, the author re-examines a model one-dimensional equation of motion for viscoelastic materials with a non-integrable memory function, with the objective of developing an existence theory which exploits the parabolic character of the equation. Existence of solutions to the initial-value problem based on coercive estimates for the linearized problem, are established both for small and large smooth date. In the former case, existence of solution is proved globally in time while in the latter case it is proved locally in time. This is a clearly written paper whose results should be of interest to those working in the field of integral equations and, to a lesser extent, to those working on viscoelastic materials.
Mathematics Subject Classification ID: 74Hxx
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 45L05
zbMATH DE Number: 4085147
zbMATH Keywords: homogeneous Dirichlet boundary conditions
zbMATH Keywords: one-dimensional equation of motion
zbMATH Keywords: parabolic character of the equation
zbMATH Keywords: initial-value problem
zbMATH Keywords: linearized problem
zbMATH Keywords: small and large smooth date
reviewed by: H. Ramkissoon
MaRDI profile type: Publication
full work available at URL: jie-1988-1-1-7
OpenAlex ID: W2018661891
description: scientific article; zbMATH DE number 4085147